Method for calibrating a measuring device

Abstract

The invention relates to a method for calibrating a measuring device for a plurality of products, having the following steps: measuring a set of measurement values for a plurality of products and with a plurality of measurements, which includes one or more measurement variables; providing a set of reference variables, which includes at least one reference variable to be determined by the measurement variables, compiling the measurement values for all products into an augmented matrix, determining a first set of calibration parameters with one or more weights for one or more products, compiling the one or more products within one product family, which has at least the same weight for its products, determining at least one further set of calibration parameters for sub-matrices of the augmented matrix, determining one or more sets with further weights within and outside the first product family, and compiling a plurality of products with the same weight into another product family, until all weights are determined for the calibration of the measuring device.

Description

TECHNICAL FIELD

[0001] The present application relates to a method for calibrating a measuring device for a product. BACKGROUND

[0002] All types of measuring devices must be calibrated before starting operation. In the context of the calibration, calibration parameters are determined for a calibration equation, for example for a linear equation, in such a way that for given measured values and the associated reference values, the best possible agreement is found. Essentially, the calibration process and the associated determination of a set of calibration parameters are known. Usually, the calibration process can also be carried out automatically.

[0003] Possible differences between the calibration relationships of different products are taken into account, for example in microwave moisture measurement technology, so far by calibrating the measuring device for each product independently of the other products. The same effort for the calibration is thus required for all products. In addition, each single calibration is equally susceptible to a possible lack of data sets, for example statistical outliers in the measurement, insufficient variation of the reference values or too low a number of measurement points. The usually chosen equation for the calibration is a multiple linear regression in which a linear relationship is assumed between the measurement variable x j and the reference variable y:

[0004] y = c1x 1、i + c2x 2、i +... + c n、i + ∈ i

[0005] (i: index of a single measurement ∈ ).

[0006] In this equation, the following expressions are customary, i.e. the factors are called weights and the additional constant is called a bias value. The epsilon value represents the measurement error that occurs in the measurement. In the context of moisture measurement technology by means of microwaves, the measurement variables are, for example, broadening of the resonance curve, shift of the resonance frequency, wetting angle, temperature value and similar quantities. The reference variables are, for such a measurement system, for example, the moisture and the density of the measured object.

[0007] The above equation for the linear regression has proven suitable for a matrix representation, in which here the following representation is derived:

[0008]

[0009] where the matrix X is

[0010]

[0011] and the vector is

[0012]

[0013] Here, the calibration parameters are distinguished from the weights c i which are multiplied with the measurement values, respectively, and the bias values c n which lead to an offset independently of the measurement values x i . The calibration parameters are determined as follows:

[0014]

[0015] The formula for determining the calibration parameters starts from the linear calibration model described above and determines the calibration parameters for the calibration model. The vector is then determined in a manner known per se, for example by means of the residual matrix, after the calibration weights have been determined.

[0016] In order to verify the significance of the calibration parameters, which is usually customary. The measure for the verification is the so-called p-value. The p-value is a measure of the plausibility for the zero hypothesis in the test theory. The zero hypothesis exists for each calibration parameter in the assumption that its value is zero. For a p-value greater than, for example, 5%, the influence of the measurement variable on the target variable is considered to be insignificant and the corresponding calibration parameter is discarded from the formula described above. This process is implemented iteratively as so-called "Feature Selection". The goal of the iterative calibration is reached when all insignificant observation variables x j have been removed from the calibration model. It is customary here to test the measurement variables of higher order, for example quadratic correlations, first and to remove the zeroth order term last.

[0017] From DE 10 2007 057 092 A1 a method for measuring humidity and / or density in a measuring object with a microwave transmitter, a microwave receiver and an evaluation unit is known. In the measurement method, the phase and the amplitude of the microwave radiation transmitted through the measuring object are determined for a plurality of frequencies, wherein a complex transmission function of the measuring object is calculated from the determined values using a transfer function of the complex values of the measuring device and is transformed into a complex time-domain function in the time domain. The time of the maximum value of the main pulse is determined as a characteristic variable A and the width of the main pulse is determined as a characteristic variable B from the time-domain function. The humidity and the density of the measuring object are determined from the characteristic variables A and B.

[0018] From DE 10 253 822 A1 a method and a device for automatic sensor calibration are known. Here, a laboratory measurement is carried out, the laboratory measurement data obtained thereby being used to correct online measurement values produced by the sensor. SUMMARY

[0019] It is the task of the present application to provide a method for calibrating a measuring device, which is suitable for simplifying the process for the calibration of a plurality of products in such a way that correlations in the data for different products are recognized.

[0020] According to the application, the task is solved by a method according to the application.

[0021] The method according to the application provides and determines a measuring device for a plurality of products for calibration. According to the application, the method has the features of claim 1. The method according to the application provides a set of reference variables Y. The set of reference variables provided contains at least one reference variable to be determined by the measuring variables. A set of measuring variables is measured in each calibration process. Here, the individual measuring variables can be distinguished by type. It can also be distinguished which product the measuring variables were recorded for and in which of the individual measurements the measuring variables were measured. A set of measurement values X p = {x p i,j} is thus produced, where j counts the one or more measuring variables, p counts the products measured and i counts the plurality of measurements. The set of measurement values is assigned a set of reference variables Y p = {y p i the i-th reference variable), which set of reference variables contains at least one reference variable to be determined by the measuring variables x P i,j The determined reference variables Y.

[0022] The method according to the application further provides that the measured variables for all products are summarized in an extended set of measured values. In a next step a first set of calibration parameters is provided, which has one or more weights for one or more products. The one or more products are summarized in a product system, if these products have at least one identical weight for their product. Identical weight means that the weight values are not significantly different from each other. The method according to the application additionally provides that at least one further set of calibration parameters is determined for a submatrix of the augmented matrix of measured values. For this purpose, one or more sets with further weights can be determined within the first product family and a plurality of products with identical weights are summarized into a further product family, thus forming a sub-product family for the first product family. Further sets with further weights are determined outside the first product family and one or more products with identical weights are summarized into a further product family. Thus parallel product families are formed, which can then naturally also form sub-product families. In these product families, the one weight or the weights are respectively associated with the measured values independently of the product. The at least one bias value is added to the association consisting of weight and measured value. The measuring device is calibrated for the extended set of measured values with respect to this set of calibration parameters. The particular idea of the application is that the measured values for two or more products are summarized and treated identically thereto.

[0023] Here, an important aspect is that it is not known before the calibration which product of the data set belongs to a product family. This correlation is also derived from the individual measured values. This equation is surprising at first, because one would really expect that the more precisely the product is defined and determined, the more precisely the measuring device can be calibrated for this product. This equation is disadvantageous in view of possible measurement inaccuracies or statistical fluctuations in the measured values. The particular advantage of the equation according to the application is that one or more weights can be found for each product, which are independent of the type of product within the product family. The weights independent of the product can be determined significantly more precisely during the calibration process than the weights based on their product correlation, which only have a small data basis. In the method according to the application, each product of a product family has precisely the property that at least one of the weights for two or more products of the product system can be determined independently of these products. This also includes the case that if two measured values are required for the measurement process to determine the output variable, a first weight is selected independently of the product and a second weight is selected in dependence on the product. In this case, the weight independent of the product can be determined statistically significantly more precisely than the weight dependent on the product.

[0024] In a further development of the method, the association of the weight with the measured value takes place by multiplication. This generally results in a linear equation for determining the quantity. Alternatively thereto, it is also possible that the weight is associated with the measured value by a polynomial or that the measured value is included together in the product and / or the quotient. Depending on the equation chosen, different calculation methods can be used for determining the calibration parameters of the first group and of the further group.

[0025] In a preferred embodiment, the significance of the determined calibration parameters is determined using their weight and / or their offset value. This is done in that for the weight and the offset value in different products the insignificance of the difference of the weight and the offset value can be ascertained. If the difference is insignificant, the values of the weight and the offset can be set to be identical. In order to test the significance in the weight and the offset value, the following null hypothesis is stated: the difference of the offset values for the two products is equal to zero. The probability of the occurrence of this null hypothesis is determined. In the test of the offset value, the difference between the two offset values or the two weights for the two products is formed. As the null hypothesis to be verified, it is then checked whether the difference has the value zero. If the null hypothesis cannot be rejected, i.e. the difference parameter thus has the value zero, the two products of the product family are set to be identical with respect to the calibration parameter (weight, offset value) examined.

[0026] In the method according to the application, the calibration parameters are determined by multiple linear regression. This is sufficiently known and can be reliably implemented. In order to distinguish the products in the data, a non-numerical category variable is added. With the category variable, it is shown, for example, that individual measured values belong to different products. The non-numerical category variable is used as a dummy variable in the augmented data matrix for distinguishing the measured values. For this purpose, a column can be appended to the augmented matrix of the measured values, which contains "1" for the individual product and is marked by "0" for the other products.

[0027] In a preferred further development, the microwave measuring device is designed as a microwave resonator, which determines the shift of its resonance frequency and / or the broadening of its resonance curve. From the two values, it is possible, for example, to determine a value for the moisture of the product. Preferably, further measured quantities, i.e. temperature and / or moisture angle, likewise contribute to the output quantity, for example the moisture of the product.

[0028] The following illustrates the application in more detail with the aid of an example. Here, the example relates to moisture measurement, as the moisture measurement is carried out with the aid of microwave measurement technology. Different products in a product family are usually only slightly distinguished from one another, for example by additional or omitted ingredients, different leaf positions on the stem in the plant or slightly changed product structures. Such slight differences and variations can lead to deviations in the binding of water molecules in the product and thus to a weak change in the calibration factor. However, stronger variations, for example by other ingredients which strongly distinguish themselves in their dielectric properties, can lead to stronger deviations in the calibration parameters. Chemical or physical similarities can be verified with the aid of adapted null hypotheses. Usually, a significance level, for example 5%, is specified for the test and compared with the p-value. The smaller the p-value, the more reason there is to discard the null hypothesis. If the p-value is smaller than the predetermined significance level, the null hypothesis is discarded. If, however, the p-value is greater than the significance level, the null hypothesis can not be discarded.

[0029] In known formulae for calibrating a measuring device, the null hypothesis is always implemented that the calibration parameter c of one product of the product family i is not distinguished from zero. It is thus possible to test the assumption that the measured parameter assigned to the calibration parameter does not contribute to the result. This assumption in determining the calibration parameter leads to the fact that one has to always observe the products of a product family in isolation. The calibration parameter is determined for each product of the product family and then tested in terms of its significance.

[0030] The method according to the application works with pooled measured parameters in which two or more products of a product family are pooled into an extended set. In this case, it is viewed in the significance test whether the difference of the calibration parameters of two products of the product family is significantly distinguished from zero. This means that for the two products the same calibration parameter can be used for calibration when the null hypothesis cannot be discarded. The calibration parameters for the two tested products of the product family are in this sense product-independent and identical.

[0031] The new null hypothesis is weaker than the conventional null hypothesis, since additional information about the similarity of the members of a product family is used in the calibration. The requirements for the quality of the data set are thus reduced and the calibration effort is correspondingly reduced. This reduction has particular advantages in practical application of the measuring device, since in the case of a slight change in the product within a product family no new calibration process is required, but the already found calibration parameter can be adapted together with new measurement values and the already existing calibration parameter is used as far as possible despite the change in the product within the product family.

[0032] What is needed in order to put this concept into practice is that the measured values obtained for the different products are summarized in an extended set of measured values. Here, the possible formulae exist in so-called dummy codes, which are also called proxy variables. Here, a variable (yes / no-variable) with the characteristic values (0 and 1) is introduced in the statistical data analysis as an indicator for the presence of a multi-level variable.

[0033] In order to mathematically consider the class configuration, for each member of the product family and for each measured variable a dummy variable of its own is introduced. For the simplest case of a linear regression with the same weight and only two classes A and B, the calibration equation takes the same form:

[0034]

[0035] In this equation, c1 denotes the calibration weight, the measured variable x i contributes with the output variable y i . The bias value c2 is expressed as a common coefficient for the classes A and B. Now there is also a distinction on the class between A and B, according to which no further bias value contributes for class A and an additional bias value Δc2 is added for class B.

[0036] The variable εi is additionally an additive expression term, which occurs together with the output variable y i and is not related to the measured value x i . The aforementioned means for class A in summary:

[0037] y i = c1x i + c2 + ε i

[0038] and for class B means

[0039] y i = c1x i + c2 + Δc2 + ε i .

[0040] With the dummy variables, the augmented data matrix is simply obtained by the additional columns in the following equation:

[0041]

[0042] ​The column to the right in the data matrix leads to the multiplication of the parameter Δc with zero for the measurement values of class A, while the measurement values of class B, i.e. the measurement values Δc, are multiplied by one. The Ipsilong parameter εi is added independently of the measurement values in order to compensate for occurring measurement errors. For this new data matrix, the p values can be calculated for the calibration parameters. Since the new calibration parameter Δc2 constitutes the difference of the bias values of the two classes, its p value gives information as to whether this difference is significant or whether the two bias values can be pooled. This pattern can be transferred to all other calibration parameters.

[0043] For the other calibration parameters, a distinction can be made between an internal development and an external development: in the internal development, the calibration parameters which have not yet been determined are determined within one product family. Here it can occur that different parameters again occur insignificantly, so that further product families are generated within the product family. For example, products 1, 3 and 5 can have the same value with regard to the first weight, i.e. only insignificantly different values; but with regard to the second weight, products 1 and 5 have the same value, while the weight for product 3 has a significantly different value. In addition to the internal development, there is also an external development, in which calibration parameters are sought for products which have not yet been pooled into one product family, for example products 2 and 4. If, for example, the same calibration parameter is found for products 2 and 4, this calibration parameter then forms the starting point for the internal development. The result of the internal and external development is that as many products as possible are pooled in product families, thereby reducing the number of calibration parameters to be determined and improving the statistical basis for the parameter determination. DETAILED DESCRIPTION

[0044] The method described above leads, using the modified null hypothesis, to the recognition of similarities in the data and their use for calibration. With the present application, a method is also proposed in which the calibration parameters of different products are pooled. It is possible in principle for some calibration parameters to be the same and others to be significantly different for products of class A and class B. In order to simplify the method, it can therefore be provided that the different parameters with the highest p values are pooled into one group, in which all calibration parameters of the two products are then set to be the same. This method can then be repeated using a reduction of the product family of one product until, for example, the calibration parameters are constant across the product family. The following is an example of the method described above: Figure 1 The present application is explained in more detail. For Figure 1 Two data sets were simulated according to the following model:

[0045] y (A) = 0.5 • x (A) + 2 + ε (A) ,

[0046] y (B) = 0.5 • x (B) + 1 + ε(B) .

[0047] The reference uncertainty ε is distributed identically for both classes with ε = + / - 0.26. This means that the data of the two classes only differ in their bias value by the value 1, but not in their slope. The data in Figure 1 is shown in Fig. 2. The upper data points (more brightly represented) have a good R 2 value of 0.894, which shows a good model match. The lower, more darkly represented values have R 2 value of 0.0239, which shows a poor match, the so-called "bad model fit". This means that the data group B with only 5 data points has a low data quality (these data points lie in a narrow area between 2.5 and 3.5) and thus does not allow the slope parameter to be reproduced accurately enough. The data group A with its 25 data points has a large numerical range together with a good quality, although the slope parameter only reaches 92% of the actual slope due to the relatively high reference uncertainty (cf. 0.4638 and 0.5).

[0048] The slope parameter cl found according to the method according to the application is, however:

[0049] cl = 0.46.

[0050] By the large difference in the weighting factor, this slope parameter is almost identical to the slope value in class A. Correspondingly, the bias parameter Δc2 differs by exactly 1, although the two bias values c2 are too large due to the slightly too small slope parameter.

[0051] In the example in Figure 1 the data values are summarized in the following table:

[0052]

[0053] It is apparent that in the conventional method the slope parameter cl is product-relatedly once 0.46 and once 0.18, and thus the slope of the model does not reach 0.5 well. The two right-hand coefficients of the table are calculated according to the method according to the application and model significantly better not only in terms of the distance of the bias values, but also in terms of the height of the values.

[0054] For the practice this means that product B, together with its low-quality data group, benefits from the good quality of the data group of product A and is thus calibrated with the same quality as product A.

Claims

1. Method for calibrating a measuring device for a plurality of products, the method having the following steps: For a plurality of products p and with a plurality of measurements i, a set of measurement values X p = {x p i,j} is measured, which set of measurement values comprises one or more measurement quantities j, a set Y of reference quantities is provided p = {y p i the i-th reference quantity}, the set of reference quantities comprising at least one reference quantity to be passed through the measurement quantity x P i,j the determined reference quantity Y, characterized in that The measured values X for all products are summarized into one augmented matrix of measured values X' P X' = (X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X12, X determining a first set of calibration parameters C', said first set of calibration parameters having one or more weights for one or more products p wherein said one or more products p are grouped within a first product family, said first product family having at least one product with the same weight c j , said weight being independent of the product, at least one further group of calibration parameters C" is determined for a submatrix of the augmented matrix of the individual measurement values X' for calibrating the measuring device, wherein Within the first product family, identify one or more groups with additional weights, and assign them the same weights. Multiple products p are grouped into another product family, and outside of said first product family are determined, and products p' having the same weight are grouped into another product family, p' are summarized into another product family, all weights are determined for the calibration of the measuring device.

2. The method of claim 1, wherein, The first group of weights and the further weights are obtained in a predetermined order, both within and outside the first product family, wherein the weights that are least strongly related to the reference variable are obtained first.

3. The method according to claim 1 or 2, characterized in that In addition to the weights, one or more bias values Δc are also determined, which are added to the measurement values multiplied by the weights.

4. The method according to claim 1 or 2, characterized in that The weights can also be associated with polynomials of the measurement values, wherein weights can also be set for products of and / or quotients of measurement values.

5. The method of claim 3, wherein, The non-significance of differences in the weights and / or bias values in different products is determined statistically, and if the differences are not significant, the different products are summarized in a product family belonging to the weight.

6. The method of claim 3, wherein, The calibration parameters are determined by multiple linear regression.

7. The method according to claim 1 or 2, characterized in that, The sub-matrices of measurement values for determining the calibration parameters are determined as subsets of measurement values X according to the first product family or the further product family. P ​ 8. The method of claim 6, wherein, In order to test the significance of the bias values, the null hypothesis is formulated as follows, namely that the difference between the bias values Δc of two products is equal to zero.

9. The method according to claim 1 or 2, characterized in that The products of a product family are entered in the measurement values by means of non-numerical class variables.

10. The method of claim 9, wherein, Virtual variables are added in order to distinguish the individual products when summarizing the augmented matrix.

11. The method according to claim 1 or 2, characterized in that A microwave measuring device is calibrated.

12. The method of claim 11, wherein, The microwave measuring device is designed as a microwave resonant cavity, which determines a shift in the resonance frequency and / or a broadening of the resonance curve.

13. The method of claim 11, wherein, A further measurement variable of the microwave measuring device is the temperature T and / or the moisture angle φ.

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